This is the basic and exam oriented question from linear equations in two variables in which we have to the cost price of a tea set and a lemon set if it is given that on selling a tea-set at 5% loss and a lemon set at 15% gain, a crockery seller gains Rs. 7. If he sells the tea set at 5% gain and the lemon set at 10% gain, he gains Rs. 13.
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 3E, question no 46
Let the cost price of the tea-set and the lemon-set be Rs x and Rs y respectively.
CaseI: When tea set is sold at 5% loss and lemon-set at 15% gain.
Loss in tea-set = Rs. 5x/100 = Rs. x/20
Gain on lemon-set = Rs. 15y/100 = Rs. 3y/20
∴ Net gain = Rs. 3y/20−x/20
⇒3y/20−x/20=7
⇒3y−x=140
⇒x−3y+140=0 (i)
CaseII: When tea-set is sold at 5% gain and the lemon-set at 10% gain.
Gain on tea-set = Rs. 5x/100 = Rs. x/20
Gain on lemon-set = Rs. 10y/100= Rs. y/10
∴ Total gain = Rs. x/20+y/10
⇒x/20+y/10=13
⇒x+2y=260
⇒x+2y−260=0 .(ii)
Subtracting equation (ii) from equation (i), we get
−5y+400=0⇒y=80
Putting y=80 in equation (i), we get
x−240+140=0
⇒x=100
Hence, the cost prices of tea-set and lemon-set are Rs. 100 and Rs. 80 respectively.